Adaption for 2-D Edge Elements in the Nonconforming Voxel Finite-Element Method

The nonconforming voxel finite-element (FE) method avoids many of the difficulties of traditional FE mesh generation using a nested grid of rectangular elements. It models arbitrary boundary shapes by adaptively refining the mesh at the boundaries. Here, the adaption is extended to reduce errors arising from elements that are away from boundaries, but are too big to represent the field adequately. The application is to 2-D edge elements for solving the time-harmonic wave equation. Results for a miter-bend waveguide and a dielectric post resonator demonstrate the effectiveness of the new algorithm.